A new fractional hybrid chaos synchronisation

Over the last decades, synchronisation of chaotic systems has become an active research area and has been extensively and intensively studied due to the variety of important applications. Different types of chaos synchronisation have been presented, and many various methods and techniques for chaos synchronisation have been reported to investigate some types of chaos. In this paper, by combining full state hybrid projective synchronisation (FSHPS) and inverse full state hybrid projective synchronisation (IFSHPS), a new type of hybrid synchronisation between different dimensional incommensurate fractional order chaotic systems is proposed. Based on fractional control laws and stability theory of linear fractional order systems, a new theorem is derived to demonstrate the co-existence of FSHPS and IFSHPS. Numerical simulations are used to validate the theoretical results.